ON CUBIC (\alpha, \beta)-METRICS IN FINSLER GEOMETRY

Abstract

In this paper, we study the class of cubic (\alpha, \beta)-metrics. We show that every weakly Landsberg cubic (\alpha, \beta)-metric has vanishing S-curvature. Using it, we prove that cubic (\alpha, \beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the Matsumoto's result for Landsberg cubic metric.